Simplify this expression: `\left(4x^{3}y^{-4}\right)^{-2}`.

Answer 1

To simplify the expression \(\left(4x^{3}y^{-4}\right)^{-2}\), we will apply the property of exponents that states \((a^m)^{-n} = a^{-mn}\) and the rule that states \((ab)^n = a^n b^n\).

1. Distribute the exponent \(-2\) to each factor inside the parentheses: \[ \left(4x^{3}y^{-4}\right)^{-2} = 4^{-2} \cdot (x^{3})^{-2} \cdot (y^{-4})^{-2} \]

2. Now simplify each part:

   • \(4^{-2} = \frac{1}{4^2} = \frac{1}{16}\)
   • \((x^{3})^{-2} = x^{-6}\)
   • \((y^{-4})^{-2} = y^{8}\) (since \(-4 \cdot -2 = 8\))

Putting these together, we have: \[ \left(4x^{3}y^{-4}\right)^{-2} = \frac{1}{16} \cdot x^{-6} \cdot y^{8} \]

3. Finally, rewrite the expression in a more standard form: \[ \frac{y^{8}}{16x^{6}} \]

Thus, the simplified expression is: \[ \frac{y^{8}}{16x^{6}} \]

Answer 2

Simplify this expression: `\left(20a^{2}b^{-12}c^{-4}\right)\left(3a^{15}b^{12}c^{6}\right)`.

Answer 3

say it in a easier way